SOLUTION OF TEIANOLES. 
409 
In the first equation cot. \ 0 may be used in the place of tan. \ (A + B). 
Case 4.— Given the three sides. Let s represent half the sum of the three 
sides = \ (a + l + c). Then any angle, as A, may be obtained from either 
of the following formulas, founded on Theorem 111: 
C0 , iA = 1 /'[^]. 
_ 2 V [s (s — a) Q — V) (s — g) ] 
The first formula should be used when A < 90°, and the second -when 
A > 90°. The third should not be used when A is nearly 180°; nor the 
fonrth when A is nearly 90; nor the fifth when A is very small. The third 
is the most convenient when all the angles are required.